In 5th generation mobile communication networks, the frequency band of the millimeter band of 30–100 GHz is supported to provide a transmission speed of 20 Gbps or higher. Furthermore, a huge transmission capacity, i.e., up to 1 Tbps, is one of the main requirements for the 6th generation mobile communication networks. In order to meet this requirement, the terahertz band is considered a new service band. Hence, we consider multi-band network environments, serving the sub-6Hz band, mmWave band, and additionally sub-terahertz band. Furthermore, we introduce the transmission point selection criteria with multiple connections for efficient multi-connectivity operation in a multi-band network environment, serving and receiving multiple connections from those bands at the same time. We also propose a point selection algorithm based on the selection criteria, e.g., achievable data rate. The proposed point selection algorithm attains lower computational complexity with a 2-approximation of the optimal solution. Our simulation results, applying the channel environment and beamforming in practical environments defined by 3GPP, show that selecting and serving multiple transmission points regardless of frequency band performs better than services through single-connectivity operation.